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Lehigh University
Lehigh Preserve
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2007
Static and seismic analysis of a single-tower cable-stayed bridge with concrete box girder
Boer LiLehigh University
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Rec%##e$ded Ca%$L, B%e', "Sac a$d e#c a$a %f a $ge-%e' cabe-aed b'dge h c%$c'ee b% g'de'" (2007). Teses and Dissertations.Pa&e' 979.
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i
Boer
and
Seismic
of a
Bridge
with
Box
September
2 7
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ST TIC ND SEISMIC N LYSIS OF SINGLE TOWERC BLE-
ST YED RIDGE WITH
CONCRETE
OX
GIRDER
by
BoerLi
Thesis
Presented to the Graduate
and
Research Committee
Lehigh University
in Candidacy
for the
Degree
Master Science
Department
Civil
and
Environmental Engineering
Lehigh University
ugust
7
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KNOWLEDGEMENTS
is a great honor and pleasure to thank the many people who made this thesis
possible.
The first person I would like
to
thank is
my
advisor Dr. Yunfeng Zhang.
the
past 2 years, his enthusiasm, creativity, and strong work ethic have made a deep
impression on me. His great effort and ability to explain abstract concepts clearly and
simply have made learning civil engineering an enjoyable experience. Throughout
my
writing of this thesis, Dr. Zhang provided inspiration, encouragement, and a lot
of
wonderful ideas. I would have been lost without him.
I would like to thank all CEE faculties, Dr. Richard Sause, Dr. James Ricles, Dr.
Yen Ben, etc. for their kind support throughout my study here at Lehigh and always
having their doors open to me when I needed it. I am eternally grateful.
I am also deeply indebted to many of
my
fellow student colleagues and friends
here
at
Lehigh for their great comradeship. The energizing and stimulating
environment that we have created together here laid the very foundation
ofthis
thesis.
I would like to thank NSF No.
e
0450300 and PITA No. PIT-547-05 for
their generous support.
Lastly, and most importantly,
my
deepest gratitude goes
to
my parents, Hong
Shao and Dr. YongSheng Li
Their unflagging love and support have enabled me to
learn and grow throughout my life. To them I dedicate this thesis.
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TABLE
OF CONTENTS
CERTIFICATE
OF
APPROVAL
ACKNOWLEDGMENTS
TABLE OF CONTENTS
LIST TABLES
LIST
OF
FIGURES
ABSTRACT
CHAPTER
INTRODUCTION
1.1
Overview
of Cable stayed Bridge
1 1 1 Conceptual description cable stayed bridge
1 1 2 Types cable stayed bridge
1 1 3 Historical development
cable stayed bridge
1 1 4 Advantages cable stayed bridge
1 1 5 Seismic performance cable stayed bridge
1.2 Research Motivation
1.3
Scope of thesis
1 3 1 Research Scope
1 3 2 Organization thesis
CHAPTER 2 THE ZHAO-BAO-SHAN
BRIDGE
2.1
Location of the
ZBS
Bridge
2.2
General
Description
2.3
Bridge Deck Structure
2.4
Stay
Cables
2.5
Bridge Tower Pylon
IV
ii
iii
iv
viii
x
3
3
3
4
4
8
8
9
9
20
3
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2 6 Foundation Bridge Pier 23
2 7 Major Construction Materials for ZBS Bridge 23
2 8 The 998 Bridge Accident
and
Corresponding Retrofit Action 24
2 8 The 998Engineering Accident
ofZ
Bridge 24
2 8 2 Retrofit Action 24
CHAPTER STATIC ANALYSIS 4
3
Introduction 4
3 Loading Cases 42
3 1 2 Load combination
44
3 2 Experimental Data
44
3 2
Field Test 44
3 2 2 Temperature induced deformation measurements 46
3 2 3 Cableforce measurements 48
3 3 Introduction
Finite Element Analysis Software
48
3 3 SAP2000 Program 48
3 3 2 Frame Element 48
3 3 3 ShellElement 49
3 3 4 Linear Static Analysis 5
3 3 5 Modal Analysis
52
3 4
FEM
Model 53
3 4 Overview 53
3 4 2 Properties ofElements
53
3 4 3 Support Conditions 53
3 4 4 Constraints 54
3 4 5 Equivalent Modulus for Cables 54
3 4 6 Initial Strains
in
Cables
55
3 4 7 Frequencies andMode Shapes
55
3 5
FEM
Linear Static Analysis Results 56
3 5 Cable forces 56
3 5 2 Stress ofDeck 57
3 5 3 Comparison with Measurements Data 59
v
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3 6 Conclusion 6
CHAPTER 4 MODEL FOR DYNAMIC ANALYSIS 88
4 Description Finite Element Model 88
4 Overview
the dynamic model 89
4 1 2 Mass Distribution 89
4 1 3 Mass Moment Inertia 9
4 1 4 Support Condition and Constraints
9
4 1 5 Equivalent Modulus for Cables 9
4 2 Modal Parameters 9
4 2 Modal Parameters
FE Model 92
4 2 2 Model Validation with Experimental Data
92
4 3 Conclusion 93
CHAPTER 5 SEISMIC RESPONSE ANALYSIS 1 7
5 Seismic Condition
the ZBS Bridge Site 1 7
5 2 Earthquake Ground Motion 1 9
5 3 Finite Element Model
and
Time History Analysis
5 4 Results and Discussion 3
5 4
Cable Forces 114
5 4 2 Bridge Tower 115
5 4 3 Bridge Deck 116
5 4 4 SelectedDisplacement and Acceleration Response Time Histories 117
5 5 Conclusion 8
CHAPTER 6 SUMMARY AND FUTURE WORK 48
6 Summary 48
6 2 Future Work 15
VI
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REFEREN ES
VIT
5
5
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LIST OF T LES
Table 1 1 Ten longest cable stayed bridges in the world
Table 1 2 Ten longest cable stayedbridges in the United States
Table
2 1
Dimension
bridge substructures
Table 2 2 Properties major construction materials
in
the
ZBS
Bridge
Table 2 3
Cable
force
values measured in September
2001
Table 3 1 Material densities
primary structural members
Table 3 2 Modal frequencies identified
from
ambient vibration test data
Table 3 3
Measured deflection
values
in bridge tower over a 3 h period
Table
3 4
Measured deflection values in bridge deck over a 3 h period
Table
3 5
Deck deformations
at
selected sections
Table 3 6 Measured cable tension force values
Table
3 7
Material properties
structural members
Table 3 8
Properties
stay cables
Table 3 9 Initial forces
and
pre strains
stay cables
Table
3 10
Modal frequencies
the ZBS
bridge calculated from
the FE model
Table 3 11 Comparison
modal frequencies
from test data and
FE model
Table
3 12
Cable forces in selected stay cables under various load combinations
Table
3 13
Comparison cable
forces with
field test
and
design values
Table
3 14
Relative change
in
selected
cable
force
from
case LC O
Table
3 15
Ratio
cable force to its yield capacity
in
selected cables under
various load combinations
Table 4 1 Mass components for a typical deck spine node
Table
4 2
Material densities
primary structural members
Table 4 3 Lumped mass and
mass
moment inertia distribution for deck
Table
4 4
Frequencies output
from
FE
model
Table 4 5 Ambient test results
Table
4 6
Frequencies results summary
V11l
12
12
27
27
28
62
62
62
62
63
66
67
68
69
71
72
95
95
95
99
99
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Table 5 Earthquake response spectrum parameters for the ZBS Bridge site 2
Table 5 2 Details
the selected earthquake records
2
Table 5 3 Scaling factor for selected earthquake records 122
Table 5 4 Comparison maximum cable force response under earthquake 123
Table 5 5 Maximum tower response at sections COl and C 2 under earthquakes 124
Table 5 6 Maximum deck response at selected sections under earthquakes
125
Table 5 7 Maximum displacement and acceleration responses at selected points 126
IX
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LIST
O IGUR S
Figure
1 1
Schematic o cable stayed bridge 13
Figure 1 2 Longitudinal layout o stay cables 13
Figure
1 3
Transverse layout
o
stay cables 14
Figure 1 4 Transverse layout o tower 14
Figure 1 5 View
o th
Stromsund Bridge in Sweden 15
Figure 1 6 View o the Ganter Bridge in Switzerland 15
Figure 1 7 View o the Tatara Bridge in Japan 16
Figure 1 8 View o the Sutong Bridge in China 16
Figure 1 9 Number o cable stayed bridges built in the United States 17
Figure 1 10 View
o
the Arthur Ravenel Jr Bridge in South Carolina 17
Figure 1 11 The Ruck A Chucky Bridge in California 18
Figure
2 1
Overall view o the ZBS Bridge from the Zhaobaoshan Hill side
Figure 2 2 Map
o
China showing the location ofNingbo City
Figure 2 3 Location o the ZBS Bridge inNingbo City 31
Figure 2 4 View
o
the estuary ofYong River 32
Figure 2 5 Elevation view o the ZBS Bridge 32
Figure 2 6 Details
o
displacement restraint device at deck/tower connection
33
Figure 2 7 GPZ basin style bearing 35
Figure 2 8 GJZF
4
plate rubber bearing 35
Figure 2 9 Standard deck cross section 36
Figure 2 10 Roadway layout on bridge deck 36
Figure 2 11 Distribution o cable forces measured in September
2 1
37
Figure 2 12 Geometry o bridge tower selected sections 38
Figure 2 13 Location
o
Segment No 16 and No 23 during accident 39
Figure 2 14 Location o retrofit section 39
Figure 2 15 Cross section o strengthened deck portion 4
Figure 2 16 Cross section o retrofit vertical web in the 49 5 m span
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Figure 3 1 Transverse layout of the ZBS bridge deck
Figure
3 2
Transducer locations in ambient vibration
test
Figure
3 3
Locations displacement survey stations
on
the
ZBS
Bridge
Figure 3 4 Locations
concrete strain gauges in selected bridge sections
Figure 3 5 Frame element
Figure
3 6
Shell element
Figure 3 7 Global view ofthe finite element model ofthe
ZBS
Bridge
Figure
3 8
Connections between tower and cables
Figure
3 9
Locations selected cables in
the
ZBS Bridge
Figure 3 10 Stress contour bridge deck in stay cable
span
under case
LC O
Figure
3 11
Stress contour bridge deck in stay cable
span
under case LC l
Figure 3 12 Stress contour bridge deck in stay cable span under case LC 2
Figure
3 13
Stress contour
bridge deck in stay cable
span
under
case LC 4
Figure
3 14
Stress contour bridge deck in stay cable
span
under
case LC 5
Figure 3 15 Stress contour bridge deck in stay cable span under case LC 6
Figure
4 1
Global view the bridgemodel
Figure 4 2 Finite element modeling ofthe cross section
the
deck
Figure
4 3
Location spine in Pier 22
Figure 4.4 Link element Friction-Pendulum Isolator)
Figure 4 5 First
four
dominant
mode
shapes from
FEM
Figure 4 6 Modal frequencies comparison-1
Figure
4 7
Modal frequencies comparison-2
Figure 5 1 Distribution
historical earthquakes in
the
study region the
ZBS
Bridge
Figure 5 2 Distribution major active earthquake faults near the bridge site
Figure
5 3
Original earthquake records
Figure 5 4 Pseudo-acceleration response spectrum
and
target
MCE
spectrum
Figure
5 5
Response spectra of scaled earthquake records
and
targetMCE
spectrum
Figure 5 6 Maximum force response in selected stay cables
Xl
73
73
74
75
77
77
8
81
81
82
83
8
85
86
8
2
3
3
3
4
6
6
127
128
129
3
3
131
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Figure
5 7
Locations
selected cross sections in tower
Figure
5 8 Maximum
bending moment and
axial force
in selected tower
sections
Figure 5 9
Maximum
bending moment and axial force response in selected
bridge
deck
sections
Figure
5 1
Displacement time history at selected locations under earthquake
KGB
Figure 5 11 Displacement time history
at
selected locations
under
earthquake
NIN
Figure 5 12 Acceleration time history
at
selected locations under earthquake
KGB
Figure
5 13
Acceleration time history
at
selected locations under earthquake
NIN
xu
3
38
39
4
142
144
146
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STR CT
This thesis deals with the static and seismic response analysis
o
a prestressed
concrete single tower cable-stayed bridge - the Zhao-Bao-Shan ZBS Bridge located
in Ningbo, China. The ZBS Bridge had a severe engineering accident on September
24,
998 and after retrofit measures it was opened to traffic on June
8
2001. In order
to
perform the analysis
o
the retrofitted ZBS Bridge, two three-dimensional finite
element models are established using
SAP2
Both finite element models were
calibrated with ambient vibration test data.
In the static analysis, various thennal differential loading cases were considered
in this study. The finite element model for static analysis employs the use
o
shell
element to model the concrete bridge deck while frame element were used for
modeling the structural members
o
the ZBS bridge. The analysis results were found
to be in good agreement with experimental survey data in terms
o
deck displacement,
tower displacement, and deck deformation and at selected locations.
Six real earthquake ground motion records were selected and scaled to
match the
maximum considered earthquake in the bridge site, where the design seismic intensity
level was raised y one degree in 2002. Nonlinear time history analysis was carried
out
to
study the seismic response behavior
o
the ZBS Bridge. A spine-model was
used for bridge deck, which is much more computationally efficient than the shell
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element model is found that
the
main structural elements the
Z S
Bridge are
still within its elastic range while potential deseating problem for bridge deck might
occur under
the selected earthquake
ground motions
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Chapter
Introduction
this chapter, an overview
o
the history and development o cable-stayed bridges n
the world well as
n
the USA is first given with the intent to offer the background
infonnation for cable-stayed bridges. The research motivation and scope
o
this thesis
on modeling and analysis
o
the Zhao-Bao-Shan Bridge, which is a prestressed
concrete cable-stayed bridge located on the east coast o China, are presented next.
Overview of Cable stayed Bridge
Conceptual Description Cable Stayed ridge
Cable-stayed bridges have become one
o
the most widely used bridge fonns in
the past three decades. Modem cable-stayed bridges present a three-dimensional
structural system that consists o girders, deck and supporting members such that
towers in compression and stay cables in tension. Schematics o a typical cable
stayed bridge as well as its main structural components are shown in Figure 1.1. As
shown in the figure, a typical cable-stayed bridge is a continuous girder with one or
more towers erected above piers
n
the middle
o
the span. From these towers, cables
stretch down diagonally usually to both sides and support the girder. Because the
only part o the structure that extends above the road is the towers and cables, cable
stayed bridges have a simple and elegant look.
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1 1 2
yp s
Cable Stayed Bridge
Cable-stayed bridges can distinguished by the number of spans, number of
towers, girder type, number of cables, etc. There are many variations in the number
and type of towers, as well as the number and arrangement of cables. Therefore,
cable-stayed bridges can also
categorized according to the construction material
used for major structural components, configurations of stay cables and tower. For
example, different types of construction materials used for the main components like
girders in cable-stayed bridges: steel, concrete, and hybrid cable-stayed bridge.
According to the various longitudinal cable arrangements, cable-stayed bridges
could be divided into the following four basic systems shown in Figure 1.2. With
respect to the positions
of
cable planes in space, there are four systems, as shown in
Figure 1.3, developed from two basic arrangements of cables: two-plane systems and
single-plane systems. Figure 1.3, the space positions of cables are: a Two vertical
planes system, b
Two inclined planes system, c Single plane system, d
Asymmetrical plane system.
Cable stayed bridges can also
classified according to various bridge towers
types: a Trapezoidal portal frames, b Twin towers, c A-frames and
d
Single
towers. Figure 1.4 shows some types ofbridge towers shapes.
1 1 3 HistoricalDevelopment
Cable StayedBridge
The idea ofusing cables to support bridge spans is by no means new, and the basic
form and concept of cable-stayed bridges have been recorded for centuries. 1617,
Faustus Verantius designed a bridge system having a timber deck supported
y
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inclined eyebars. 1823 the
famous
French engineer Navier developed bridge
systems stiffened by inclined chains.
The other type stay arrangement with parallel stays was suggested by Hatley
dating back to 1840.
1868
the Franz Joseph Bridge over the Moldau River
at
Prague Czech was built using a new fonn suspension introduced in the bridge.
Although cable stayed bridges have been around for the last couple
centuries
they have become more prevalent in the last
50
years. Over the past decades rapid
development
has
been made on modem cable stayed bridges with application
high strength materials
and new
methods construction development electronic
computers and progress
in
structural analysis.
The first modem cable stayed bridge was
the
Str6msund Bridge designed by
Franz
Dischinger.
The
Str6msund Bridge built in
1955
in
Sweden
is a reinforced concrete
bridge with a main span
182.6
m.
The Str6msund Bridge consists
two portal
towers and two vertical planes
double radial stays
as
shown
in
Figure
1.5.
The
Ganter Bridge crossing an Alpine valley is located near the Simplon Pass in
Switzerland
as
shown
in
Figure 1.6. Built in 1980 the Ganter Bridge is an interesting
example
cable stayed bridge though the cables are inside a thin concrete shell.
The
overall layout the bridge is S shaped in plan the 174m main span is straight but
the side spans including
the
back stay cables have
200 m
radius curves. The taller
pier is
50
m high.
Cable stayed bridges
are
very price competitive in the 150 600 m span lengths
range.
Modem cable stayed bridges with increasing main span length and more
shallow and slender girders are adding more challenges to the structural design and
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analysis for bridge engineers. Table
provides a list o cable-stayed bridges with
the longest main span throughout the world.
The Tatara Bridge is the world s longest cable-stayed bridge as o Year 2006
as
shown in Figure 1.7. The Tatara Bridge was opened to traffic in 1999 connecting the
islands o Honshu and Shikoku across the Seto Inland Sea in Japan. is a steel
girder cable-stayed bridge. The bridge measures 1480 m in total length and has an
890-m long main span. The cables
o
the bridge are placed to make a
fan
shape and
the steel towers
o the bridge are 220 meters high and shaped like an inverted Y. The
main towers have a cross-shaped section with comers cut for enhanced wind stability
and more attractive architectural appearance.
Sutong Bridge is located at lower Yangtze River linking Nantong City and Suzhou
City in China. This steel-girder cable-stayed bridge is still under construction
presently and is scheduled
to
open
to
traffic in 2008. After completion the bridge s
main span which is 1088-m long will exceed that o th Tatara Bridge by 198 meters.
is anticipated that the Sutong Bridge will keep the record o the world s longest
stayed-cable bridge for a considerable period o time. The Sutong Bridge is
comprised o twin A-shape towers stay cables in semi-fan arrangement and a steel
deck as shown in Figure
8
n
the United States there has been a substantial increase in the number and the
rate
o
construction
o
cable-stayed bridge in the past two decades. Table 1.2 lists the
cable-stayed bridges with ten longest main span lengths in the United States. The
oldest cable-stayed bridge in the United States is the Sitka Harbor Bridge built in
1970 near Juneau Alaska. From 1996
to
2005
7
cable-stayed bridges were built in
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the United States. Figure 1.9 shows the number of cable-stayed bridges built in the
United States from 1955 to 2005 in 10-year increments Tabatabai 2005).
The Arthur Ravenel Jr. Bridge crossing the Cooper River, shown in Figure 1.10, is
presently the longest cable-stayed bridge in the United States, with a 471-m long
main span. is also the longest bridge of its kind in the North America. The Arthur
Ravenel Jr. Bridge has a cable-stayed design with semi fan cable arrangement and
two diamond-shaped towers, each with a height of 175
m
The span was designed
to
endure wind gusts in excess
of
300 mph 133 mls far stronger than those of the
state s worst hurricane, Hugo 1989)
nd
withstand a magnitude 7.4 earthquake on
the Richter scale without total failure.
Another interesting example of cable-stayed bridge is the Ruck-A-Chucky Bridge
s shown in Figure 1.11. This bridge is considered to the most famous bridge
never built. The would-be bridge location is ten miles upstream of the Auburn Dam
in California. The bridge design has a V-shaped curved flat deck, supported by
numerous cables anchored on the sloping hillsides on each side of the gorge. There
are no towers and no supporting piers below the roadway. The bridge is designed
to
consist
of
two components: the cable stays acting in tension and the curved girder
carrying the traffic and absorbing the axial compression produced y the cables. The
conception and design of this bridge represents an achievement in modem bridge
engineering whereby technology in its many respects is rationally and inter
disciplinarily applied to transform
n
environmental obstacle into an asset, thus
arriving at an economical as well as
n
aesthetic solution.
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1 1 4Advantages
Cable Stayed Bridge
The rapid development cable stayed bridge can be partially attributed t its
many outstanding characteristics and advantages. Cable stayed bridge designs are
used for intermediate length spans and fill the gap that exists between the girder type
and suspension type bridges. Compared with suspension bridge cable stayed bridge
has the advantages ease construction lower cost since anchorages are not
required and small size substructures; furthermore there are no massive cables
s
with suspension bridges which making cable repair or replacement much easier in
cable stayed bridges. The general trend suggests that cable stayed bridges with longer
span length are becoming possible and economically more advantageous than
suspension bridges.
1 1 5 Seismic Performance
Cable StayedBridge
Earthquakes can have a very serious effect on a bridge.
can cause damage t
structural elements cause vibrations through the bridge
r
even lead to a bridge
collapse. Understanding the seismic response behavior cable stayed bridges is thus
important to ensure structural safety and improve future design. Most cable stayed
bridges have a number long period modes due t the flexibility their cable-
superstructure system. However in a seismic environment since the largest
earthquake spectral accelerations typically occur at relatively short periods cable-
stayed bridges with fundamental periods starting from 2.0 seconds tend t have a
degree natural seismic isolation. Thus a rather favorable combination structural
dynamics and ground motion characteristics often exists for these types
bridges
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Weso10wsky and Wilson 2003).
In
the United States, two long-span cable-stayed
bridges - the Bill Emersion Bridge n Missouri and the Arthur Ravenel Jr. Bridge in
South Carolina are located in seismic active region. The Bill Emerson Bridge, a new
Mississippi River crossing in service since December 2003, is located approximately
80 ndue north o New Madrid, Missouri. The New Madrid area, where the great
earthquakes o
8
and 1812 occurred, is an active seismic region requiring
earthquake hazard mitigation programs. Design o the bridge accounted for the
possibility o a strong earthquake magnitude 7 5 or greater) during the design life o
the bridge, and as a result was based on design response spectrum anchored to a zero
period acceleration ZPA) o 0.36 g with a 10 probability
o
being exceeded in 250
years Woodward-Clyde 1994). A state-of-the-art seismic monitoring system with 84
accelerometers was installed to this 1,206-m-Iong 3,956 ft) Bill Emerson Memorial
Bridge in 2003 Celebi 2006).
2
ese rch
Motivation
This research is focused on modeling and analysis o a single-tower prestressed
concrete cable-stayed bridge in China - the Zhao-Bao-Shan ZBS) Bridge under
static gravity and thermal differentials) and earthquake loading. The ZBS Bridge is
selected for this study because o the following reasons: i) The ZBS Bridge has a
very unique configuration - single-tower with asymmetric main and side spans,
which warrants a detailed study
o
its structural behavior under various loading
conditions such as thermal differential and earthquakes; Although cable-stayed bridge
has become more and more popular in the US, thus far there is no bridge
o
this kind
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in the Unite States. The current analysis will provide valuable infonnation on the
structural behavior o the ZBS Bridge, and also help with the future application o
this kind o cable-stayed bridges in the Unite States. ii The ZBS Bridge had a severe
engineering accident during the construction see Section 2.8 for details : concrete
crushed at the lower flange o its prestressed reinforced concrete RC bridge box
girder; after the accident and subsequent retrofit, structural properties
o
the bridge
are supposedly different from the original design. Modeling o the bridge after retrofit
is necessary to reflect the true behaviors o the bridge at present and predict its
behavior under future loading such as heavy trucks and earthquakes. iii Last but not
least, the region - Ningbo City in China, where the ZBS Bridge is located, has
moderate earthquake activity. According to the Chinese seismic design code, the peak
ground acceleration specified for this region classified
as
a Degree VII for seismic
intensity level is equal
to
2.25 m/sec
is worth noting that in Year 2002, the
seismic design intensity level in the local area o the
ZBS
bridge site was adjusted
from Degree VI to VII. Since its constructionwas completed
n
2001, the ZBS Bridge
was thus designed for a seismic intensity level lower than that specified
n
the current
seismic design code. n order
to
assure the safety o ZBS bridge under earthquakes
loading, nonlinear time history analysis is thus necessary to provide an important
basis for the estimated seismic response o the ZBS bridge, especially after the
engineering accident in 1998 and subsequent retrofit actions taken on the bridge.
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3 Scope
Thesis
3
esearch Scope
This thesis presents the results
modeling and analysis
a single towered RC
cable stayed bridge the ZBS Bridge located on the east coast China. Two
versions three dimensional finite element models were established for the ZBS
Bridge using the SAP software. The first one is a sophisticated finite element
model based on the use
shell elements for the concrete bridge box girder and was
used for static analysis the
Z
bridge. The other one is based on beam elements
and was used for nonlinear time history analysis
the ZBS Bridge under
earthquakes. Both static analysis and dynamic analysis the Z Bridge were
performed in this study. Modeling details
as
well
as
the results from the static
analysis and dynamic analysis are discussed in this thesis.
3 2rganization Thesis
There are six chapters in this thesis. Chapter 1 provides an introduction to the
history and development cable stayed bridges as well as the research motivation
and scope
this thesis. Chapter 2 gives a description
the ZBS Bridge.
Chapter
3 both the modeling details as well as the static analysis results for the ZBS Bridge
are discussed. Chapter 4 presents the finite element model for dynamic analysis the
Z Bridge. Chapter 5 discusses the results from nonlinear time history analysis
the ZBS Bridge under earthquakes. Lastly Chapter 6 provides a summary and
suggests possible work for future research.
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ble Ten longest cable stayed bridges in
the
world
No. Bridge name
Main span
m
Location
Country
Year
1 Sutong
1088 Suzhou Nantong
China 2009
2 Stonecutters
1018
Hong Kong China 2008
3
Tatara
890
Hiroshima Japan 1999
4
Pont
de
Normandie
856
LeHavre France
1995
5
Incheon-2
800
Incheon Songdo South Korea 2009
6
Nanjing-3
648
Nanjing
China
2005
7
Nanjing 2
628
Nanjing
China
2001
8
Jintang
620
Zhoushan Island
China
2008
9
Baishazhou
618
Wuhan
China
2000
10
Qingzhou 605
Fuzhou
China
2003
Table
2
Ten longest cable stayed bridges in
the
United States
No.
Bridge name
Main span
Location Year
m
1 The Arthur Ravenel
Jr.
Bridge 472 South Carolina 2005
2 Greenvill Bridge
US
82 over Mississippi 420 Mississippi
2005
3
Dame Point Bridge
397
Florida 1989
4 Fred Hartman/Houston
Ship
Channel
381
Texas
1995
5 Sidney Lanier Bridge Brunswick
381
Georgia 2003
6
Hale Boggs/Luling Bridge
373
Louisiana 1984
7
Sunshine Skyway Bridge
366
Florida
1987
8 William Natcher/Owensboro Bridge
366
Kentucky
2002
9
Bill Emerson/Cape Girardeau Bridge
351
Missouri
2003
10
Talmadge Memorial Bridge Savannah
336
Georgia
1991
Year bridge construction completed
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Side span L
Tower
Main
spanL
Tower
Side span
Ll
Figure
Schematic
of
cable stayed bridge
SINGLE DOUBLE TRIPLE
MUTIPLE
VARIABLE
STAY
~ Y S T
1 3 5
BUNDLE
OR
1
CONVERGING
R RADIAL
ARP OR
- r r
PARALLEL
3
FAN
r
STAR
Figure
2
Longitudinal layout
of
stay cables Troitsky
1988
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~
: C = = =
oll
Figure 3Transverse layout stay cables Troitsky 1988
a Two vertical planes system b Two inclined planed system
c Single plane system d Asymmetrical planed system
2
3 4
5
I I
Figure 4Transverse layout
tower Troitsky 1988
1 Portal frame tower 2 Twin monolithic tower 3 Twin frame tower
4 A-frame tower 5 Single tower 6 Side tower
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igur 5 View
ofthe
Stromsund
Bridge
in Sweden
Troitsky
988
igur 6 View
of
the Ganter
Bridge
in Switzerland
Courtesy
http://en.structurae.de
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Figure
7
View
the Tatara Bridge
in
Japan Courtesy ofhttp://www.answers.com
Figure 8 View the
Sutong
Bridge in China Courtesy ofhttp://www.roadtraffic-
technology com
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18
: r . . .
16
14
1.2
IJIl
10
ij
.S::
CD 8
5
6
z
4
.2
o
96
97 98
1990 2000
More
Years
Figure
1.9 Number
of cable-stayedbridges built
in the United
States
Tabatabai 2005
Figure
1.10
View ofthe ArthurRavenel Jr. Bridge
in
South Carolina Courtesy of
http://ravenelbridge.net
17
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igur The
Ruck-A-Chucky Bridge in California Courtesy of
http://www.ketchum.org
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Chapter
The Zhao Bao Shan Bridge
This chapter provides a general description
o
the Zhao-Bao-Shan Bridge hereafter
referred to as ZBS Bridge , a reinforced concrete cable-stayed bridge with a 258-m
main span and a single tower. A brief description o an engineering accident that
occurred during the construction o the ZBS Bridge as well
as
the corresponding
retrofit actions taken to strengthen the bridge are also given in this chapter.
2
Location of
the ZBS Bridge
The ZBS Bridge crosses the Yong River at its estuary, connecting the
Zhao-Ban-Shan and Jin-Ji-Shan in Ningbo, China, as shown in Figure 2.1. Ningbo
City is located on the east coast o China, as shown n Figure 2.2. Figure
2 3
shows
the location o the ZBS Bridge in the local region o Ningbo City. Complex terrain
conditions exist at the site o the ZBS Bridge, which consists o a piedmont marine
alluvial plain and denudation buttes. The Jin-Ji-Shan hill on the east side
o
the ZBS
Bridge, has a gradual slope except for some steep slopes due
to
man excavation; The
Zhao-Bao-Shan hill on the west side o the bridge, has steep slopes and even cliffs at
some locations. The altitudes o the top
o
both hills are about 8 m in terms
o
the
Yellow Sea Altitude Level. The piedmont marine alluvial plain was formed during
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the latter part of the Holocene Epoch and
it
has gradual terrain with the ground
altitude being around 2.5 m to 3.5 m.
The Yong River is about 450 m wide at the location of the ZBS Bridge. A view
of
the estuary
of
the
ong River is shown in Figure 2.4. The main navigational channel
is on the west-central side
of
the Yong River and has a water depth of 7 to
1 m
Due
to the tide effect, its east side is an alluvial bank with a 150-m wide muddy tidal
marsh. The geological bedrock at the bridge site consists
of
an upper layer with
felsophyre and a lower
tuff
sandstone layer. On top of the bedrock, there lies a 14 to
33 m deep silt layer as well as a muddy clayblanket.
2.2 eneral escription
The ZBS Bridge is a prestressed concrete cable-stayed highway bridge with a main
span
of258
m, a side span
of
185 m and approach structures, totaling 568 m. has a
single tower with a height
of
148.4 m. The ZBS Bridge was open to traffic
on June
2001, after a construction period of six years.
As shown in Figure 2.5, the main structural system ofthe ZBS Bridge is composed
of prestressed concrete box girder, reinforced concrete tower and high-strength steel
cables. There are a total
of
six piers No. 20 to No. 25 in Figure 2.5) that are aligned
to a straight line. No. 22 pier is the main pier that supports the bridge tower, from
which the bridge deck surface has a 3 down slope in the longitudinal direction on
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both sides. The span configuration is 74.5 m west approach span 258 m main
span 185 m side span 49.5 m side span . The navigation channel is right
beneath the main span
the bridge. The clearance for the navigation channel
the
bridge is 32 m, which permits the passage
5000-ton ships. There are transverse and
longitudinal displacement restraint device on top
No.
22
pier see Figure 2.6 ,
pot-shape rubber bearings Model No.GPZ at No. 20, 21 24,
25
piers see Figure
2.7 , and special tension-compression bearings Model No.GJZF4 plate rubber
bearing at No.
23
pier see Figure 2.8 . There are expansion joints Model
No.SSFB400 in the ZBS Bridge located at PierNo. 20 and
No
25 respectively.
The ZBS Bridge carries six lanes traffic, with a design speed 60 km h for the
traffic. The design traffic volume the bridge is 40,000 to 50,000 vehicles per day.
The bridge is designed to resist wind over Grade 12 with a maximum wind speed
greater than 32.6 sthe design wind speed for bridge deck and tower is 40.3 s
and 46.5 srespectively . Additionally, a total eight ash transmission pipes with a
diameter
219
mm
each are placed in the longitudinal direction along the middle
line the bridge.
3ridge Deck tructure
A standard cross section
the prestressed concrete box girder
the ZBS Bridge
is shown
in
Figure 2.9. The ZBS Bridge has six traffic lanes, totaling 29.5 m in width.
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The prestressed concrete box girder has a height o 2.5 m with a standard section
made up o double cells on the side, a single cell and an open section in the middle.
Also, the layout o the carriageway on the deck is shown in Figure 2.10. The
configuration
o
the traffic lanes is 1.5 m buffer zone 11.25 m for three traffic
lanes 4.0 m ash pipe zone 11.25 m for three traffic lanes 1.5 m buffer zone .
The prestressed concrete box decks are made o C50 concrete cube compressive
strength
=
50 MPa, see note below Table 2.2 .
4Stay Cables
The 102 cables are made o high-strength stranded steel wires. 7-mm galvanized
steel wires are used. The smallest cross-sectional area
o
the cables is 4195 mm
2
,
and
the largest cable cross-sectional area is 11583 mm
2
The stay cables are covered with
a
5
to 8-mm polyethylene sheath for corrosion protection. The typical spacing
between the cable anchors is 8.0 m at the bridge deck and 2.0 m at the tower. The
cable forces under dead load only from the maintenance and management manual for
the
ZBS
Bridge are listed in Table 2.3. Also, the cable forces from measurement and
design values are also presented in Figure 2.11.
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5
Bridge Tower Pylon
The height the ZBS bridge tower is 148.4 m. The tower is H shaped. Each
tower leg supports a total
5
stay cables. The tower is made
C50 concrete with a
cube compressive strength
f u k
equal to 50 MPa. The cross sections
the tower at
selected locations along its height are shown in Figure 2.12.
6Foundation
Bridge
Pier
The foundation the ZBS bridge piers consists deep rock socketed friction
end bearing bored piles with varying diameters. The deepest embedded length the
piles is 30 m the bedrock. The pile caps are also deeply embedded in soil. The pile
cap
the bridge towers made large volume concrete is located below the
construction water level by 5 meters. Table 2.1 provides a detailed list
the
dimensions
all bridge substructures.
7
Major Construction
Materials for
ZBS Bridge
The properties the major construction materials used in the ZBS Bridge are
summarized in Table 2.2.
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2 8 The 998 ridge ccident and Corresponding Retrofit Action
2 8
The 1998 Engineering Accident ofZBS Bridge
The construction
of
the ZBS Bridge started in
y
1995. On September 24, 1998,
an accident happened in the ZBS Bridge when No.
23
segment
of
the bridge s
prestressed concrete box girder was being built and the main span of the bridge was
2 m away from closure. At the time
of
the accident, the bottom flange plate, inclined
web plate and vertical web plate of the concrete girder crushed at the location ofNo.
6
segment. The locations of No. 23 segment and No. 6 segment are illustrated in
Figure 2.13. Immediately after the accident, a series
of emergency measures were
taken to stabilize the damage condition
of
the bridge and protect the bridge from
further damage.
8 Retrofit Actions
After the bridge condition became stable after taking emergency measures, the
following retrofit actions were made
n
the main span and side span respectively to
strengthen the bridge ZBS Bridge Maintenance Management Manual 2002).
1) Main Span
i Partial Removal: nine 8-m long segments in the prestressed concrete box
girder as well as 36 stay cables were removed from the bridge. The
removed sections are No. 5 to No. 23 segments as shown in Figure 2.14.
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ii Strengthening: As seen in Figure 2.14, the part
o
the bridge deck between
Segment 14 and No.24 pier were preserved and strengthened. The length
o
this whole section is 305 m. Two longitudinal composite beams with
embedded channel steel shapes were added at the comer location
o
the
box girder cells. Additionally, the thickness o the inclined web plates in
the bridge deck was increased
y
10 cm. The details are shown in Figure
2.15.
iii Rebuilding: No.15 to
5
deck segments, a 3.5-m transition segment on the
Zhao-Bao-Shan side, and a 1.5-m closure segment
in
the main span were
rebuilt. Additionally, a total
o
44 stay cables were replaced in the
retrofitted bridge. A standard cross section
o
the rebuilt bridge deck is
illustrated in Figure 2.9 a .
2 49.5-m Side Span this span is located between No. 24 and No. 25 piers
i Removal: The redundant concrete blocks located on
both sides
o
the
bridge deck were cut
y
80 cm to reduce the transverse internal force
in
the upper flange
o
the bridge deck. The removed part measures 39.84 m
in
length, from a point lO-m away from Pier 24 to Pier 25.
ii Strengthening: The thickness
o
a 12-m long bottom flange plate
o
the
bridge deck was increased
y
8 cm. Additionally, four longitudinal
diaphragms and two vertical webs were added to the bridge deck along the
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retrofitted side span. The details of these vertical webs are illustrated in
Figure 2.16.
On October 22 1999 construction
of
the main span
of
the ZBS Bridge was
completed. The removal and retrofit project was also successfully finished. From
March
to April 10 2001 the main structure
of
the ZBS Bridge was inspected
by
the Highway Engineering Test Center
of
the Ministry of Transportation. The field
inspection program included static test live load test and ambient vibration test.
Based
on
the test results the bridge is considered to satisfy the criteria
of
the China
bridge design code.
On
May 9 2001 nineteen bridge engineering experts visited and
evaluated the condition
of
the ZBS Bridge. was concluded that overall the retrofit
project was of a good quality. The ZBS Cable stayed Bridge was opened to traffic on
June 2001.
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Table 2 Dimension bridge substructures
PierNo. Piles
Pile D Pile
Cap
Beam
Pier Column Pier Cap Beam
m
m
m
m
20
8 1.5 24x7.8x3.0
3x4, t= 0.8 28.24x3.0x4.0
21 14
2.0 24.5x17x3.5
3x4, t=
0.8
22.50x3.Ox4.0
22 20
2.5 40x20x5.5 Tower
-
23
8 1.5 19.5x7.8x3.0
3x4,
t= 0.8
24 8 1.5
19.5x7.8x3.0
3x4,
t= 0.8
20.40x3.Ox4.0
25 8 1.5
19.5x7.8x3.0 3x4, 0.8 27.l0x3.0x4.0
Note: D = diameter
t
=
wall thickness Pier column is made up
hollow reinforced concrete section)
Table Properties major constructionmaterials in the
ZBS
Bridge
Materials
Strength Elastic Modulus Density
Structural Member
MPa
MPa
Kg/m
3
)
Concrete C50
f u k =
50
3.45E+04
2500
Deck, Tower
Concrete C30
f u k
= 30
3.00E+04
2500
Pier
Steel f
y
= 1670 2.00E+05
7849
Stay Cable
Note: The measure concrete quality is its compressive strength. Compressive strength test is based
on the use
cube specimen with a dimension
150 x 150 x 150 mm. Cube-shaped impermeable
molds are filled with concrete during the concrete placement process as specified by the China
Concrete Code GB50010-2002. The cubes are then moisture-cured for
28
days, and tested at a
specified loading rate after completion
28-day curing. The compressive strength obtained from such
test specimens is termed cube compressive strength feu
k
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ble 2.3
Cable force values measured
September
2001 adapted
from Z S
ridge
Maintenance
Management Manual 2002)
Measured Cable Force (kN)
No.
Design Value (kN)
Upstream Downstream
Force Error Force
Error
Cl
2303 2494 8.29 2577 11.90
C2
2475
2716
9.74 2758
11.43
C3
2418
2605 7.73
2183
-9.72
C4 2333
2332 -0.04 2318 -0.64
C5
2532 2533 0.04 2563 1.22
C6
2706 2791 3.14 2797 3.36
C7
2917 2943
0.89
2986 2.37
C8
3429 3432 0.09 3566 4.00
C9
3138 3135 -0.10
3157
0.61
CI
3443 3439 -0.12 3508 1.89
Cl1
3607 3659
1.44
3637 0.83
C12 3239 3287 1.48 3290 1.57
C13 3653 3692 1.07 3769 3.18
C14 3654 3721 1.83 3721 1.83
C15 4164
4229 1.56
4217 1.27
C16 4342 4388 1.06 4351 0.21
C17 4172 4223 1.22 4183 0.26
C18
4167,
4173 0.14 4110 -1.37
C19 4186 4215 0.69 4327 3.37
C20 3951
3981 0.76
4001 1.27
C21
4329 4275 -1.25 4393 1.48
C22 4923
4867
-1.14 4921 -0.04
C23 5366 5302 -1.19 5331 -0.65
C24 5662
5407 -4.50
5449
-3.76
C25 5775
5597 -3.08
5552
-3.86
Cl 2163 2311 6.84 2419 11.84
C2 2349 2482 5.66 2433 3.58
C3
2582
2606 0.93
2615
1.28
C4
2634 2622
-0.46 2600 -1.29
C5
2216 2384 7.58 2295
3.56
C6
2728 2849 4.44 2847
4.36
C7
2919 3085 5.69
3037
4.04
C8 3099 3328 7.39
3345
7.94
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Measured Cable Force (kN)
No.
Design Value kN
Upstream Downstream
Force
Error Force
Error
C9
3250 3457
6.37 3363 3.48
C10
3553
3705
4.28 3649 2.70
ll
3498 3597 2.83
3655
4.49
C12 3094 3206 3.62 3227 4.30
Cl3 3991
4069 1.95 3874 -2.93
C14 3624 3771
4.06 3573 -1.41
C15 4143 4278 3.26
4229
2.08
C16 3922 3934 0.31
3899 -0.59
Cl7 3765
3779 0.37 3762 -0.08
C18 38 3898 2.02
3829
0.21
C19 4317 4343 0.60
4283 -0.79
C20 4281
4169 -2.62 4292 0.26
C21 4536 4456 -1.76 4420 -2.56
C22
5157
4939 -4.23
4981
-3.41
C23
5357
5473
2.17
5605
4.63
C24 5902
5805
-1.64
5865
-0.63
C25 5865
5841 -0.41
5708 -2.68
CO
4759
4977 4.58 4980 4.64
29
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igur
2
Overall view
the
ZBS
Bridge from
the ZhaobaoshanHill side
downloaded from http://forestlife.info
igur
2 2 Map
China showing
the location ofNingbo City
Courtesy
Microsoft MapPoint
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SE OND EXPOSURE
Figure
2
Overall view of the ZBS Bridge from the Zhaobaoshan Hill side
downloaded from http://forestlife.info)
S < t
[iL
-
; / r 0 ~ q l
XINJI NG
\
V ~ -
U l a ~ n b a d t ~ r ~ . .. .
MONGOLI
Figure
2.2
Map of China showing the location ofNingbo City Courtesy
of
Microsoft MapPoint)
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igur
3
ocation
the
ZBS Bridge
in
Ningbo City
Courtesy
icrosoft
MapPoint
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SE OND EXPOSURE
angzhou W m
ng.han
h lu wang
X,epu
g .han
ho chen
U C 1 ~ O t t
a p o i n s ~
Figure 3 Location of the ZBS Bridge Ningbo City Courtesy of Microsoft
MapPoint
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Figure
4 View
of
the
estuary
ofYongRiver
745 258
2
83
495
Unit mm
in i han
Zhao ao han
Figure
5Elevation view
of
the
ZBS
Bridge
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= 5==
2=2 :: 5_ - - - j
700/2
75
I . _ = ~ ~ = _ . ;
700/2
75
Deck
Tower
Bearing
L . . 1 ~
(a) Elevation
view of
the longitudinal displacement restraint
device
Bearing
I f
~ t _ I r . . . . . r _ _ I r _ _ . . . . . r r _ f _ _ 1
...........
1i / ; ;
IU:
, ,.t Jtt _- I ~ r A 0 0
f
~
~
40
30
124/2
124/2
30
40 36
Tower
. J . . - - - - - - - - - - - - - - - - r - ' - - - - - - - ~ ~ ~ - - - - - - -
b)
A-A section of the longitudinal displacement restraint device
Figure
2.6 continued)
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------.----r---------
c
Elevation view of the transverse displacement restraint
device
Deck
Tower
d D-D section of the transverse displacement restraint device
Figure 6 Details of displacement restraint
device
at deck tower connection
ZBS
Bridge
Maintenance
ManagementManual 2002
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J: :m
upper
\ iH1l1 lB l
se. lling bbetring
_
V J l ~ f f t J J i cOon ing
pla c
- I ( i l l : l : J i i ~ in lia c b3ring plate
- - - l l i ~ J F
scalingri
~ - l l l < l . k t u b b e r b l \(
< >-1':,,,,,10.,
Figure 7
GPZ
basin-style bearing CourtesyofTongji University
China)
Figure 8 GJZF
4
plate rubber
bearing
Courtesy ofTongji University
China)
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1 5
t
5
~ e t f ~ n r
J ~
yeF
75
l 275
450 437.5 237.5
135 2
450
275
2950/2 2950/2
1/2 cross
echon ofdouble
box double
cell girder 1/2cross section
double box
smglccell
girder
a Cross-section of rebuilt bridge
deck
1/2 cross section
double box double cell girder
1 5
25
1/2 cross section
double
box single cell
girder
135 2
o
t
437.5
295 2
450
1.5
~ ~ 1 I I 1
t ~ : : : l
b Cross-section
of
preserved bridge
deck
Figure 2 9
Standard
deck
cross section
2950
150
1125 400 1125
Cable
Rail
Rail
Pavement
Cable
Anchorage Anchorage
Vehicle
Vehicle
Lanes Area Lanes Area
Figure 2 1
Roadway layout on bridge deck
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7000
6000
-
I esign Vol... I
:::::::::J ro v.lJo upoIroun
04000
3000
2000
1000
(1)5000
o
LL
I
o
0 ' ' ' ' ' '1 ' 1 '1'1'1' 1 1 1 ' . ,1 , . , .,1,.,111,11.,.,111111 1111 1111 111111 1I11111111111111
C25C24C23C22C21C20C19C18C17C18CI5C14CI3C12Cl1Cl0C9 C8 C7 C8 C5 C4 C3 C2
Cl CO
Cl C3 C4 C5 C6 C7
Cll
C9'C1O'C11'C12'C13CI4C15Cl8'CI7'CI8'CIe'C20'C21C22I::23C24C25'
No. of Cable
(a) Upstream cable plane
3000
7000
-6000
- 5 0 0 0
I
o
LL
I
: 0 2 000
o
1000
I_DesignV- I
:::::::::J oaurod
o _m
0 1 I,., I
I
1 1, . , . , . , . , . , . ,1 , 1111 1111 111I1111 1I111111 1I11111I11 II II 1111111I11 11111I11111111 II
C25C24C23C22C21C20CI9C18C17C18C15C14C13C12Cl1Cl0C9 C8
C7 C8 C5 C4 C3 C2 Cl co Cl
C3'
C4 C5 C6 C7 Cll
C9'C1O'C11'C12C13C14C15Cl8'C17'C18'C1e'C20'C21C22'C23C24C25'
No.
of
Cable
(b) Downstream cable plane
Figure 2.11 Distribution of cable forces measured in September 2001 (ZBS Bridge Mainte.nance Management Manual 2002)
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I
~
G
G
~
r
0
E
E
I
I
G
I
t 700 t
i
1
t
A-A
120
120
C
C
~
IF
r
0
q
q
q
H
75
500
500
B B
C-C
A
A
0 0
0
0l 50
B 50
I
r
0
0
k
6 0
E-E
G-G
H-H I I
Figure 2.12
Geometry bridge tower
selected
sections
unit: cm
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Zhao aa Shan
Jin Ji
Shan
Unit m
Figure 2 3 Location
Segment No 6
and
No 23
during
accident
Zhao aaShan
Part I ast in site concrete transition section
Part II losure section
Part III
Rebuilt section
Part
IV
ase
in
site concrete
transition section
PartV
Preserved section
Figure
2 4
Location
retrofit
section
39
JinJi Shan
Unit m
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2 0 4 0 2 0
5
T
N>I
N
0
00
N
0
N l )
00
>
N
.....
e28e
150
342
1350/2
2934/2
Figure
2 5
Cross section of strengthened deck portion
Unit:
cm
T
5
n
~
I
0
Additional
l )
N
vertical web
r
61
I
l
42
450 450 450/2
2934/2
Figure 2 6
Cross section of retrofit vertical web in the 49.5 m span Unit: cm
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Chapter
Static nalysis
This chapter deals with a three-dimensional finite element model developed for static
analysis the Zhao-Bao-Shan ZBS Cable-stayed Bridge using the SAP
software. Modeling details as well as the results static analysis are presented in this
chapter.
3 Introduction
The objective this finite element based static analysis is three-fold,
as
described
below,
i Static analysis is carried out
to
better understand the behavior
cable
stayed bridge structures under a variety
loading conditions such as dead
load, temperature change, and load combinations.
ii Field test data from the as-built bridge is used to validate the finite element
model, which can then be used to predict the response
the bridge
structure under various loading conditions.
iii The results
static analysis provide essential data such as the deflected
equilibrium shape
the bridge deck for subsequent dynamic analysis.
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3 Loading Cases
Two types loads are considered here: dead load and temperature load. The
details
these loads are given in the following sections.
1 Dead load
Two types
dead loads are considered in this study: i primary dead load from
structural elements and secondary dead load due to gravity
nonstructural elements.
Primary dead load refers to the gravity loads structural members such as bridge
decks, tower i.e., pylon , piers, cables, and etc. The material densities
the primary
structural members are listed in Table 3.1.
Secondary dead loads are gravity load nonstructural elements placed on the
bridge structure after concrete hardened, which include bridge railings, transmission
pipes, pavement, and etc The arrangement these nonstructural elements is
illustrated Figure 3.1.
The dead loads considered for the cable-stayed bridge this study can be
classified as,
a
Weight per unit volume for concrete: 24.500 kN/m
3
b Weight per unit volume for steel stay cable : 76.920 kN/m
3
c Ash transmission pipe in operation : 2.176 kN/m per pipe
d Ash transmission pipe not in operation : 1.676 kN/m per pipe
e
Water transmission pipe: 5.600 kN/m per pipe The ash and water
transmission pipes are idealized as
a concentrated load which is applied in
the center
bridge deck
f
Bridge guide rails: 1.250 kN/m per rail The guide rails are idealized
as
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four concentrated loads that are applied in the center and the sides of
bridge deck
g Pavement: 57.516 kN/m The pavement has a thickness of 80 mm and is
modeled as uniform load on the deck
2 Temperature load
Temperature variations are considered in this study to examine the responses of
bridge stay cables and concrete structural members under thermal loadings. The
thermal expansion coefficient of steel is 1.17E-5 1C while this coefficient is 1.00E
1C for concrete. Thermal differentials between the top and bottom surfaces of the
concrete deck are also included in this study.
A
total of
the
following five cases are considered for the thermal loading in this
study,
a Temperature Load
T
the temperature of the whole bridge increases
by
25C
b Temperature Load II T : the temperature of the whole bridge decreases
by
25 C.
c Temperature Load III T3 : the temperature of the stay cables increases
by
5Cwhile the temperature
of
other parts
of
the bridge does not change.
d Temperature Load IV T4 : the temperature of the stay cables decreases by
15C while the temperature ofother parts of the bridge does not change.
e Temperature Load V T
s
:
the temperature
of
the bottom surface of the
bridge deck decreases by 5C while the temperature of the deck top surface
remains unchanged.
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3 1 2 Load combination
VariOllS load cases are considered to account for the combined effect
of
dead loads
and temperature change. Details of
the individual load cases
can be
found in the
previous sections.
a Load Combination 0 LC O): Dead Load only
b) Load Combination 1 LC l): Dead Load + Temperature Load I D+T
t
c) Load Combination 2 LC 2): Dead Load + Temperature Load II
D T
z
d) Load Combination 3 LC 3): Dead Load + Temperature Load III D+T
3
)
e) Load Combination 4 LC 4): Dead Load + Temperature Load D+T
4
)
f
Load Combination 5 LC 5): Dead Load + Temperature Load
V
D+T
s
)
3.2
Experimental Data
3.2.1
Field Test
n extensive series of ambient vibration tests were conducted to measure the
dynamic response
of
the ZBS Bridge from March 20, 2001 to April 10, 2001 ZBS
Bridge Maintenance Management Manual 2002). Conducting full-scale dynamic
tests on bridge is one of the most reliable ways of assessing the actual dynamic
properties of cable stayed bridges. The main objective was to experimentally
determine the dynamic properties
of
the ZBS Bridge
by
conducting an ambient
vibration test
on
the full-scale bridge using wind, water, etc. as the sources
of
random
excitation without any traffic-induced loading or periodic vibration sources. The
dynamic properties
of
principal interest are modal frequencies, mode shapes and
information on damping of the structure.
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A computer-based data acquisition system was used to collect and analyze the
ambient vibration data. The instrumentation system consisted the following
components: i a total
28
vibration transducers Model 891 from Institute
Engineering Mechanics, Harbin, China were placed at strategic locations on the
bridge. These transducers with built-in amplifier can convert the ambient vibration
velocity or acceleration signal into electrical signal. ii Cabling was used to
transmit signals from transducers to the data acquisition system. iii Signals were
amplified and filtered by signal conditioner.
To accurately identify the mode shapes
the bridge, locations the vibration
transducers must be carefully selected before the vibration test. In the ambient
vibration test conducted by the Highway Engineering Inspection Center
the
Department Transportation, China ZBS Bridge Maintenance
Management
Manual 2002 , vibration transducers were placed at the quarter points
the main
span and mid points the other spans. Therefore, a total 28 vibration transducers
were placed along both the upstream side and the downstream side
the bridge deck.
The location
these transducers on the bridge deck is illustrated in Figure 3.2.
The modal frequencies and mode shapes
the first four dominant modes were
identified for the bridge structure. Also, estimations were made for damping ratios
based on ambient vibration test data. The experimental data indicates the occurrence
many closely spaced modal frequencies and spatially complicated mode shapes.
Table 3.2 lists four modal frequencies the ZBS Bridge identified from the
experimental data, which correspond to the dominant vertical, lateral, longitudinal
and torsional modes, respectively. The modal frequencies
the first vertical, lateral,
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longitudinal and torsional modes are 0.406 Hz, 0.564 Hz, 0.742 Hz and 0.957 Hz,
respectively. The dynamic properties
o
the ZBS Bridge are characterized
as
low
frequency vibration and small damping ratio.
3 2 2 Temperature induced
eform tion
measurements
A field survey
o
the
ZBS
bridge deflections was conducted y the Institute
o
Communication Science Technology at Zhejiang University, China, from 4:00 AM
on August
th
,
2001
to
10:00 AM on August
9
t
2001 after the bridge construction
was completed ZBS BridgeMaintenance Management Manual 2002). During this
survey, the bridge was closed to any traffic and the weather condition on these two
days was sunny. Bridge deflection data were collected for the tower and the bridge
deck. The measurement locations are indicated
in
Figure 3.3. The experimental data
was processed using computers and measured values o the relative deflection for the
tower and the bridge deck are summarized in Table 3.3 and Table 3.4, respectively.
The following observations were made from the experimental measurements:
i) Lateral and Longitudinal Displacement o
Tower: From Table 3.3, the
tower displaced horizontally towards the west direction when the
temperature increased. The tower returned to its initial position at 4:00 AM
on the next day.
ii) Longitudinal Displacement
o
Deck: As seen in Table 3.4, there is a
tendency that the two sides
o
the deck i.e., main span and side span)
extended westward and eastward, individually, with the increase
o
environmental temperature. Averagely speaking, the elongation
o
the west
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side main span) was about 1.7 times that ofthe east side side span). the
meanwhile, with the decrease
of
the temperature, the deck deflected in the
reverse direction. was observed that the deck almost returned to its initial
configuration at 4:00 AM on the next day.
An
elongation peak value of 14
mm
occurred in the main span deck near pier 21 at 16:00 PM on August
18,2001.
On August 10, 2001, a total
of
86 concrete strain gages were installed to the
selected locations inside the box girder cells
of
the ZBS Bridge in order to measure
its thermal response behavior. Gauges were installed at five selected bridge sections
in the main and side spans,
as
shown in Figure 3.4. Two sets ofmeasurements were
taken in different seasons: first measurements taken at 7:00
A M
on August, 13th,
2 1
and second measurements taken at 10:00
A M
on January 12th, 2002. The
measured temperature was 18C and 30C for the first and second measurements,
respectively. The relative changes in strain measurements are listed in Figure 3.5.
Using the measured strain and temperature data, sectional restraint stresses and
continuity thermal stresses were calculated. However, effects of creep and shrinkage
in reducing the effective modulus of elasticity, thereby relieving the thermal
continuity stresses, were not considered. is seen from Table 3 5 that temperature
change causes strain in the bridge deck and for the
2C
temperature difference.
The average value of thermal strain is -115
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3 2 3 Cableforce measurements
In April 2001, after the completion o the ZBS Bridge, the initial cable forces o
the bridge under dead load only were measured
y
the Highway Engineering
Inspection Center
o
the Department
o
Transportation, China ZBS Bridge
Maintenance
Management Manual 2002 . The experimentally measured cable
force data are shown in Figure 3.6. The design cable forces are also listed
in
Table 3.6
for comparison purposes.
3.3
Introduction Finite lement nalysis Software
3 3 1 SAP2 Program
SAP2 version 1 is utilized in this study for static and dynamic analysis
o
the ZBS Cable-stayed Bridge. The SAP programs were originally developed
y
Dr.
E L
Wilson et
a
at University o California, Berkeley. With a 3D object-based
graphical modeling environment and nonlinear analysis capability, the SAP2
program provides a general purpose yet powerful finite element analysis software
program for structural analysis. This computer program is one
o
the most popular
structural analysis software packages used
y
structural engineers in the USA.
3 3 2 Frame Element
The frame element in SAP2 uses a general, three-dimensional, beam-column
formulation, which includes the effects o biaxial bending, torsion, axial deformation,
and biaxial shear deformations. Structures that can be modeled with this element
include three-dimensional frames, three-dimensional trusses, cables, and etc.
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A frame element
is
modeled as a straight line connecting two points.
The
frame
element activates all six degrees o freedom
at
both o its connected joints. Each
element has its
own local
coordinate system for defining section properties and loads,
and
for
interpreting output. Figure 3.5 illustrates the
frame
element in the global
coordinate system.
Material properties, geometric properties and section stiffness
are
defined
independent
o
the frame elements and are assigned to the elements. Each frame
element
may be loaded by gravity in any direction , multiple concentrated loads,
multiple distributed loads strain loads, and loads due to temperature change.
frame elements are
supposed not to transmit
moments
at the
ends
the geometric
section properties
j
i
and
in can be set to zero, or both bending rotations, R
and
R3
at both ends and the torsional rotation,
j
at either end can be released.
a dynamic
analysis
the mass
o
the structure
is used to
compute inertial forces.
The mass contributed by the frame element is lumped
at
the joints
i
and
j
No inertial
effects.
are
considered within the element itself. The total mass
o
the element is equal
to
the integral along the length
o
the mass density
m
multiplied by the cross
sectional area a plus the additional mass per unit length, mpl The total mass is
applied to each o the three translational degrees of
freedom:
UX UY and UZ. No
mass moments
o
inertia are computed
for
the rotational degrees o freedom.
3 3 3 Shell Element
The Shell element is a
three
or four-node formulation that combines separate
membrane
and plate-bending behavior. The
four joint
element does not have to be
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planar. The membrane behavior uses
an
isoparametric formulation that includes
translational in-plane stiffuess components and a rotational stiffuess component in the
direction normal to the plane ofthe element.
The plate bending behavior includes two-way, out-of-plane, plate rotational
stiffuess components and a translational stiffuess component in the direction normal
to the plane of the element.
y
default, a thin-plate Kirchhoff formulation is used
that neglects transverse shearing deformation. Alternatively, a thick-plate
Mindlin/Reissner formulation can
be
chosen which includes the effects of
transverse shearing deformation.
Structures that can
be
modeled with this element include three-dimensional shells
e.g., tanks and domes , plate structures e.g., floor slabs , and membrane structures
e.g., shear walls . Each Shell element in the structure can be used to model pure
membrane, pure plate, or full shell behavior. The use of full shell behavior is
generally recommended unless the entire structure is planar and is adequately
restrained.
Each Shell element has its own local coordinate system for defining Material
properties and loads, and for interpreting output. Temperature-dependent orthotropic
material properties are allowed. Each element may be loaded
by
gravity and uniform
loads in any direction; surface pressure on the top, bottom, and side faces; and loads
due to temperature change.
Each Shell element and other types of area objects/elements may have either of
the following shapes, as shown in Figure 3.6: i Quadrilateral, defined
by
the four
joints j
andj
ii Triangular, defined by the three joints jl j2, and
h,.
The
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Shell element always activates all six degrees
of
freedom at each of its connected
joints.
In a dynamic analysis, the mass of the structure is used to compute inertial forces.
The mass contributed
y
the Shell element is lumped at the element joints.
o
inertial
effects are considered within the element itself. The total mass
of the element is equal
to the integral over the plane of the element
of
the mass density, multiplied by the
thickness,
t
The total mass is applied to each
of
the three translational degrees
of
freedom: UX, UY, and UZ. No mass moments of inertia are computed for the
rotational degrees of freedom.
4 Linear Static Analysis
Static analyses are used to determine the response of the structure to various types
of
static loading. These load cases may include: self-weight loads on frame and/or
shell elements, temperature loads, etc.
The linear static analysis of a structure involves the solution of the system oflinear
equations represented y Equation 3.1:
u
r
3.1
where
K
is the stiffuess matrix, r is the vector of applied loads, and is the vector of
resulting displacements.
For each linear static analysis case, a linear combination ofone or more load cases
can be defined to apply in the vector r. Most commonly, a single loads case in each
linear static analysis case can be solved and the results maybe combined later.
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As a load case, temperature load creates thermal strains in the frame and shell
elements. These strains are given by the product
o
the material coefficients o
thermal expansion and the temperature change o the element. Two kinds o
temperature loads can be specified: uniform temperature change and temperature
gradient. The temperature change may be different for individual element in each
load case. Temperature load cases are utilized to simulate the environmental
temperature difference for the structure in the analysis.
3 3 5 odal nalysis
Modal analysis is used to detennine the vibration modes
o
a structure. These
modes are useful in model calibration with experimental data and calculation
o
equivalent lateral seismic load for the structure.
There are two types o modal analysis to choose when defining a modal analysis
case in SAP2 : i Eigenvector analysis determines the undamped free-vibration
mode shapes and frequencies
o
the system. These natural modes provide some
insight into the behavior o the structure. ii Ritz-vector analysis seeks to find modes
that are excited y a particular loading. Ritz vectors can provide a better basis than
do
eigenvectors when used for response-spectrum or time-history analyses that are based
onmodal superposition.
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4 FEM Model
3 4 Overview
this study, a three-dimensional finite element
modell
for the ZBS cable-stayed
bridge is developed using SAP2000 version 10.0.0, as shown in Figure 3.7. This
finite element model has a total 59070 nodes, 1104 frame elements and 62906
shell elements. More specifically, 58062 nodes and 62906 shell elements are used for
the bridge deck; the bridge tower has 356 nodes and 352 frame elements; 549 nodes
and 544 frame elements are used for the five bridge piers. The stay cables are
modeled using 204 nodes and 2 frame elements. Additionally, 134 nodes and 106
frame elements are employed to model the rigid links in this finite element model.
For example, as shown in Figure 3.8, rigid links were used to connect the actual cable
anchoring point with the corresponding tower nodes.
3 4 2 Properties
lements
The material properties structural members are listed in Table 3.7.
3 4 3 Support onditions
Boundary conditions at the base
Piers 20, 21, 22 tower), 23, 24 and 25
are specified such that their motion are restricted in all directions, i.e., they are
modeled as fixed end supports.
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3.4.4 Constraints
Constraints are applied to restrict the deck from moving in the longitudinal,
vertical and lateral direction and rotating around x axis in Pier 20, 21, 23, 24 and
25 while Pier 22, the tower, is assigned with translational constraints
longitudinal and lateral directions and rotational constraints around x axis.
temperature load cases analysis, the longitudinal constraints are released
in
Pier 20,
21, 23, 24 and 5 in order to simulate the thermal response behavior of the
bridge deck on the friction bearings at the top of these piers.
3.4.5Equivalent odulusfor Cables
When modeling the stay cables, the catenary shape and its variation with the axial
force in the cable are modeled with an equivalent elastic modulus. The stay cable can
modeled with a truss element that has a modified modulus
of
elasticity, E
eq
, given
y Ernst Equation Ernst 1965).
E
E
e
3.2
1 [ WLxYAeEe]
12T
3
e
where
A
e
is area of the cross-section,
T
c
is the tension in the cab